SubmissionNumber#=%=#30 FinalPaperTitle#=%=#Do Soft Prompts Have Useful Wavelet Structure? Negative Evidence In A Controlled Setup ShortPaperTitle#=%=# NumberOfPages#=%=#12 CopyrightSigned#=%=#Bamdev Mishra JobTitle#==# Organization#==# Abstract#==#Soft prompts are learned embedding sequences, but nothing guarantees that their token axis behaves like a signal with useful coarse and fine structure. We test that premise with the Discrete Wavelet Transform (DWT), which rewrites a sequence into approximation (coarse, low-frequency) and detail (local, high-frequency) coefficients. Wavelets help images and audio when most squared coefficient mass concentrates in the approximation band and the detail coefficients become sparse. Trained soft prompts meet neither condition. Our primary test decomposes a converged soft prompt into DWT bands, fine-tunes one band or both, and compares against a matched-budget baseline that continues vanilla training with no DWT. A constructed positive control first confirms that the procedure recovers a target displacement when the displacement is confined to the trainable band and rejects it when the required band is frozen. On SST-2 (67K) and AG News (120K) with Haar wavelets, and on an SST-2 check with Daubechies-2, no band-selective mode reliably beats the baseline, and the two bands are interchangeable within 0.2~pts. Direct measurement of the converged prompt finds coefficient mass roughly balanced across the bands and detail coefficients far denser than classical wavelet theory expects. Related variants behave the same way. An end-to-end wavelet prompt tuner does not reliably outperform vanilla, and a token-diversity variant makes prompt tokens more diverse without improving accuracy. On 250 held-out FLAN generation examples, existing Wavelet KD and Standard KD checkpoints are indistinguishable under token F1 and ROUGE-L. Author{1}{Firstname}#=%=#Soumyadeep Author{1}{Lastname}#=%=#Dey Author{1}{Orcid}#=%=# Author{1}{Email}#=%=#Soumyadeep.Dey@microsoft.com Author{1}{Affiliation}#=%=#Microsoft Author{2}{Firstname}#=%=#Srikanth Author{2}{Lastname}#=%=#Tenneti Author{2}{Username}#=%=#stenneti Author{2}{Orcid}#=%=# Author{2}{Email}#=%=#stenneti@microsoft.com Author{2}{Affiliation}#=%=#Microsoft Author{3}{Firstname}#=%=#Bamdev Author{3}{Lastname}#=%=#Mishra Author{3}{Username}#=%=#bamdevm Author{3}{Orcid}#=%=# Author{3}{Email}#=%=#bamdevm@gmail.com Author{3}{Affiliation}#=%=#Microsoft Author{4}{Firstname}#=%=#Shobhit Author{4}{Lastname}#=%=#Niranjan Author{4}{Orcid}#=%=# Author{4}{Email}#=%=#shniranjan@microsoft.com Author{4}{Affiliation}#=%=#Microsoft Author{5}{Firstname}#=%=#Mayur Author{5}{Lastname}#=%=#Datar Author{5}{Orcid}#=%=# Author{5}{Email}#=%=#mayurdatar@microsoft.com Author{5}{Affiliation}#=%=#Microsoft ========== èéáğö